Uniform truncation error for Shannon sampling expansion from local averages

Abstract

Let \(B_\Omega ^p \), 1 ≤ p ≤ ∞, be the set of all bounded functions in Lp(ℝ) which can be extended to entire functions of exponential type Ω. The uniform bounds for truncation error of Shannon sampling expansion from local averages are obtained for functions \(L^p (\mathbb{R})\) with the decay condition $$\left| {f(t)} \right| \leqslant \frac{A} {{\left| t \right|^\delta }},t \ne 0, $$ where A and δ are positive constants. Furthermore we also establish similar results for non-bandlimit functions in Besov classes with the same decay condition as above.